3^-2 divided by 3^6

Answer 1

To simplify this expression, we need to first rewrite the base of the exponents as the same number:

3^-2 = 1 / 3^2 (using the property a^-n = 1/a^n)

Now we can rewrite the division as a subtraction of exponents:

1 / 3^2 ÷ 3^6 = 1 / 3^(2-6) = 1 / 3^(-4)

Finally, we can rewrite the negative exponent as a positive exponent by moving the base to the denominator:

1 / 3^(-4) = 1 / (1 / 3^4) = 3^4 = 81

Therefore, 3^-2 ÷ 3^6 = 1.